The twisted Satake isomorphism and Casselman-Shalika formula
arXiv:1307.7510
Abstract
For an arbitrary split adjoint group we identify the unramified Whittaker space with the space of skew-invariant functions on the lattice of coweights and deduce from it the Casselman-Shalika formula.
9 pages. The previous version has been replaced. Thanks to Yiannis Sakellaridis for his comments